Evolution of inelastic plane curves
This short note discusses geometric flows for planar curves, of the form \(\partial F/\partial t = f T + g N\), which are `inelastic' or locally arclength-preserving; \(f\) and \(g\) are functions of the curvature \(\kappa\). The main results are that for such flows \(\partial f/\partial s= g\kappa\), and \(\partial \kappa/\partial t = \partial/\partial s(f\kappa +\partial g/\partial s)\). These, however, are easy consequences of formulas that appeared in papers by \textit{J. Langer} and \textit{D. Singer} [J. Differ. Geom. 20, 1-22 (1984; Zbl 0554.53013)] and \textit{J. Langer} and \textit{R. Perline} [J. Nonlinear Sci. 1, 71-93 (1991; Zbl 0795.35115)] -- and elsewhere, no doubt. The note concludes with three short examples.
scientific article; zbMATH DE number 1369313